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Exponent, Roots, And Logarithm Slide 3: If we replace the base a by a, the exponents 4 and 5 by positive integers m and n : We will get: am = a.a.a….a m times an = a.a.a….a n times am.an = (a.a….a).(a.a….a) m times n times = a.a.a……..a (m+n) times FORMULA I with condition a € R, a ? 0 a is called the base number and m,n is called exponent Slide 4: if m>n, them use formula I, we shall obtain: am-n .an = am-n+n am-n .an = am Formula II an Slide 5: pay attention the following problem : (am)n = am.am…..am n times = am+m+m….m = am.n Conclusion Formula III Slide 6: If besides a we also use the base of b, then the form (ab)m. Can be defined : (ab)m = ab.ab……ab m times = (a.a.a.a).(b.b.b.b) m times m times Formula IV Slide 7: So that by the same way we will get Conclusion : b? 0 Formula V Because : is not defined Example : Simplify! : Example : Simplify! Slide 10: Answer Slide 13: B.Integers Exponents In this section we shall see that formula I-V hold for integers exponents, either positive, negative and zero If we substitute m = n use formula II we shall obtain Formula VI a € R, a ? 0 Slide 14: If we subsituty m=0 use formula II we will get Formula VII a € R, a ? 0 Slide 15: SIMPLIFY!! Examples Slide 17: Answer Slide 20: By the Formula I we obtain am.an = am+n If we substituting n=m, then we will get am.am = a2m so that a2m = a 2m =1 m =1/2 form a2m =a ,can be changed (am) 2 = a am = va a1/2 = va In general can written C. Fractional Exponent Slide 21: In the fractional exponents: If is changed ,then we will get : n,m is positive integers Formula VIII Slide 22: By the formula VIII: ,then if ,we obtain Formula IX Furthermore the formula I - IX,also hold for fractional exponents Slide 23: Example Simplify and write down in positive exponents! Slide 24: Simplify and write down in the roots form ! Slide 25: 3. Evaluate! Slide 26: 4. Find the length of diagonal of rectangle if it has dimension length is cm and width is cm! Slide 27: Answer Slide 33: EXPONENT EQUATION Example : 1. Find the solution set : Slide 34: Answer Slide 35: Example : 1. Find the solution set : Slide 36: Answer Slide 38: Example : 1. Determine the solution set : Slide 39: V Answer Slide 40: : 2 V Slide 41: V V Slide 42: D. Rational Numbers and Irrational Number (1) Rational Number Rational Number are numbers which can be put in a/b form with a and b are integers numbers and b ? 0. Example: 3 coz 3 can be stated in etc 0.444…= 0.4 can be stated in 1.12 can be stated in Notes ! The lines above 12(no.3)shows that 12 is repeated unlimitedly Generally ! Rational number are repeated decimals Slide 43: (2) Irrational Numbers Irrational number are number which can’t be stated in Generally : Irrational numbers are unrepeated decimal Example! =1.4142135…. = 5.1461524…. Log 2 = 0.3010…. e =2.71828182….. coz can’t be put in Slide 44: 1.Please check whether the following form are rational or irrational. Examples Slide 45: Answer Slide 46: E. Root Form Root number are the rational number which the result are irrational EXAMPLE : Slide 47: 1. Please check whether the following forms are root forms or not Note : Ln = Log number with base e Ln x = elog x Excercise Slide 49: Answer Slide 51: ANSWER Slide 52: Answer Slide 53: E. Algebra Operation Of Root Form REMEMBER !! Slide 54: 1. Evaluate the value of the following root forms ANSWER Examples Slide 55: Answer Slide 57: 1. Find the value of the following problem !! 2. Find 2p+2q, 4pq and p2+q2 ANSWER Home Work !!! Slide 58: Answer Slide 62: G. Rationalizing The Denominator A fractional of root on its denominator such as : Can be simplified by rationalizing Slide 63: Examples Slide 65: Logarithm Formula Excercise Logarithm Slide 66: Logarithm Formula Slide 67: BACK Logarithm Formula Slide 68: ANSWER 1. EVALUATE !! Excercise Slide 69: Answer Slide 73: NEXT Slide 74: 2. SIMPLIFY !! ANSWER Slide 75: Answer Slide 76: NEXT Slide 77: EVALUATE !! ANSWER Slide 78: NEXT Answer Slide 79: ANSWER Slide 80: Answer Slide 82: NEXT Slide 83: 5. Find the value of x that fulfill of the following equation! ANSWER Slide 84: TM Answer Slide 86: 1. Find the value of x that fulfill of the following equation !! ANSWER Home Work !!! Slide 87: Answer Ø Slide 89: V Slide 90: V Slide 91: thanks for your Attention...! cReated by: alFAth and NUgz el-Saverzs united You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.